The Brin-Thompson groups sV are of type F_\infty

We prove that the Brin-Thompson groups sV, also called higher dimensional Thompson's groups, are of type F_\infty for all natural numbers s. This result was previously shown for s up to 3, by considering the action of sV on a naturally associated space. Our key step is to retract this space to a subspace sX which is easier to analyze.Comment: Final version, in Pacific J. Math., 10 pages, 4 figure

Exponential localization of singular vectors in spatiotemporal chaos

In a dynamical system the singular vector (SV) indicates which perturbation will exhibit maximal growth after a time interval $\tau$. We show that in systems with spatiotemporal chaos the SV exponentially localizes in space. Under a suitable transformation, the SV can be described in terms of the Kardar-Parisi-Zhang equation with periodic noise. A scaling argument allows us to deduce a universal power law $\tau^{-\gamma}$ for the localization of the SV. Moreover the same exponent $\gamma$ characterizes the finite-$\tau$ deviation of the Lyapunov exponent in excellent agreement with simulations. Our results may help improving existing forecasting techniques.Comment: 5 page

Estimation of Stochastic Volatility Models : An Approximation to the Nonlinear State Space

The stochastic volatility (SV) models had not been popular as the ARCH (autoregressive conditional heteroskedasticity) models in practical applications until recent years even though the SV models have close relationship to financial economic theories. The main reason is that the likelihood of the SV models is not easy to evaluate unlike the ARCH models. Developments of Markov Chain Monte-Carlo (MCMC) methods have increased the popularity of Bayesian inference in many fields of research including the SV models. After Jacquire et al. (1994) applied a Bayesian analysis for estimating the SV model in their epoch making work, the Bayesian approach has greatly contributed to the research on the SV models. The classical analysis based on the likelihood for estimating the (SV) model has been extensively studied in the recent years. Danielson (1994) approximates the marginal likelihood of the observable process by simulating the latent volatility conditional on the available information. Shephard and Pitt (1997) gave an idea of evaluating likelihood by exploiting sampled volatility. Durbin and Koopman (1997) explored the idea of Shephard and Pitt (1997) and evaluated the likelihood by Monte-Carlo integration. Sandmann and Koopman (1998) applied this method for the SV model. Durbin and Koopman (2000) reviewed the methods of Monte Carlo maximum likelihood from both Bayesian and classical perspectives. The purpose of this paper is to propose the Laplace approximation (LA) method to the nonlinear state space representation, and to show that the LA method is workable for estimating the SV models including the multivariate SV model and the dynamic bivariate mixture (DBM) model. The SV model can be regarded as a nonlinear state space model. The LA method approximates the logarithm of the joint density of current observation and volatility conditional on the past observations by the second order Taylor expansion around its mode, and then applies the nonlinear filtering algorithm. This idea of approximation is found in Shephard and Pitt (1997) and Durbin and Koopmann (1997). The Monte-Carlo Likelihood (MCL: Sandmann and Koopman (1998)) is now a standard classical method for estimating the SV models. It is based on importance sampling technique. Importance sampling is regarded as an exact method for maximum likelihood estimation. We show that the LA method of this paper approximates the weight function by unity in the context of importance sampling. We do not need to carry out the Monte Carlo integration for obtaining the likelihood since the approximate likelihood function can be analytically obtained. If one-step ahead prediction density of observation and volatility variables conditional on the past observations is sufficiently accurately approximated, the LA method is workable. We examine how the LA method works by simulations as well as various empirical studies. We conduct the Monte-Carlo simulations for the univariate SV model for examining the small sample properties and compare them with those of other methods. Simulation experiments reveals that our method is comparable to the MCL, Maximum Likelihood (Fridman and Harris (1998)) and MCMC methods. We apply this method to the univariate SV models with normal distribution or t-distribution, the bivariate SV model and the dynamic bivariate mixture model, and empirically illustrate how the LA method works for each of the extended models. The empirical results on the stock markets reveal that our method provides very similar estimates of coefficients to those of the MCL. As a result, this paper demonstrates that the LA method is workable in two ways: simulation studies and empirical studies. Naturally, the workability is limited to the cases we have examined. But we believe the LA method is applicable to many SV models based on our study of this paperStochastic volatility, Nonlinear state space representation

On Leverage in a Stochastic Volatility Model

This paper is concerned with specification for modelling financial leverage effect in the context of stochastic volatility (SV) models. Two alternative specifications coexist in the literature. One is the Euler approximation to the well known continuous time SV model with leverage effect and the other is the discrete time SV model of Jacquier, Polson and Rossi (2004, Journal of Econometrics, forthcoming). Using a Gaussian nonlinear state space form with uncorrelated measurement and transition errors, I show that it is easy to interpret the leverage effect in the conventional model whereas it is not clear how to obtain the leverage effect in the model of Jacquier et al. Empirical comparisons of these two models via Bayesian Markov chain Monte Carlo (MCMC) methods reveal that the specification of Jacquier et al is inferior. Simulation experiments are conducted to study the sampling properties of the Bayes MCMC for the conventional model. the appropriateness of statistical arbitrage as a test of marketefficiency.Bayes factors; Leverage effect; Markov chain Monte Carlo; Nonlinear state space models; Quasi maximum likelihood.

Space station utilization and commonality

Several potential ways of utilizing the space station, including utilization of learning experiences (such as operations), utilization of specific elements of hardware which can be largely common between the SS and Mars programs, and utilization of the on-orbit SS for transportation node functions were identified and discussed. The probability of using the SS in all of these areas seems very good. Three different ways are discussed of utilizing the then existing Low Earth Orbit (LEO) SS for operational support during assembly and checkout of the Mars Space Vehicle (SV): attaching the SV to the SS; allowing the SV to co-orbit near the SS; and a hybrid of the first 2 ways. Discussion of each of these approaches is provided, and the conclusion is reached that either the co-orbiting or hybrid approach might be preferable. Artists' conception of the modes are provided, and sketches of an assembly system concept (truss structure and subsystems derivable from the SS) which could be used for co-orbiting on-orbit assembly support are provided

Estimating Stochastic Volatility Models Using a Discrete Non-linear Filter. Working paper #3

Many approaches have been proposed for estimating stochastic volatility (SV) models, a number of which are filtering methods. While non-linear filtering methods are superior to linear approaches, non-linear filtering methods have not gained a wide acceptance in the econometrics literature due to their computational cost. This paper proposes a discretised non-linear filtering (DNF) algorithm for the estimation of latent variable models. It is shown that the DNF approach leads to significant computational gains relative to other procedures in the context of SV estimation without any associated loss in accuracy. It is also shown how a number of extensions to standard SV models can be accommodated within the DNF algorithm.non-linear filtering, stochastic volatility, state-space models, asymmetries, latent factors, two factor volatility models

Parameterisation and Efficient MCMC Estimation of Non-Gaussian State Space Models

The impact of parameterisation on the simulation efficiency of Bayesian Markov chain Monte Carlo (MCMC) algorithms for two non-Gaussian state space models is examined. Specifically, focus is given to particular forms of the stochastic conditional duration (SCD) model and the stochastic volatility (SV) model, with four alternative parameterisations of each model considered. A controlled experiment using simulated data reveals that relationships exist between the simulation efficiency of the MCMC sampler, the magnitudes of the population parameters and the particular parameterisation of the state space model. Results of an empirical analysis of two separate transaction data sets for the SCD model, as well as equity and exchange rate data sets for the SV model, are also reported. Both the simulation and empirical results reveal that substantial gains in simulation efficiency can be obtained from simple reparameterisations of both types of non-Gaussian state space models.Bayesian methodology, stochastic volatility, durations, non-centred in location, non-centred in scale, inefficiency factors.

Seasonal overturning of the Labrador Sea as observed by Argo floats

Author Posting. © American Meteorological Society, 2017. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 47 (2017): 2531-2543, doi:10.1175/JPO-D-17-0051.1.Argo floats are used to investigate Labrador Sea overturning and its variability on seasonal time scales. This is the first application of Argo floats to estimate overturning in a deep-water formation region in the North Atlantic. Unlike hydrographic measurements, which are typically confined to the summer season, floats offer the advantage of collecting data in all seasons. Seasonal composite potential density and absolute geostrophic velocity sections across the mouth of the Labrador Sea assembled from float profiles and trajectories at 1000 m are used to calculate the horizontal and overturning circulations. The overturning exhibits a pronounced seasonal cycle; in depth space the overturning doubles throughout the course of the year, and in density space it triples. The largest overturning [1.2 Sv (1 Sv ≡ 106 m3 s−1) in depth space and 3.9 Sv in density space] occurs in spring and corresponds to the outflow of recently formed Labrador Sea Water. The overturning decreases through summer and reaches a minimum in winter (0.6 Sv in depth space and 1.2 Sv in density space). The robustness of the Argo seasonal overturning is supported by a comparison to an overturning estimate based on hydrographic data from the AR7W line.NSF OCE-1459474 supported this work.2018-04-1